A topological model for the Fukaya categories of plumbings

Details A topological model for the Fukaya categories of plumbings A topological model for the Fukaya categories of plumbings

2009-04-09

arxiv.org/abs/0904.1474v3

Mathematics

Symplectic Geometry

67 pages, 12 figures, incorporated referee comments, and changed the discussion of compactness

Scientific paper

We prove that the algebra of singular cochains on a smooth manifold, equipped with the cup product, is equivalent to the A-infinity structure on the Lagrangian Floer cochain group associated to the zero section in the cotangent bundle. More generally, given a pair of smooth manifolds of the same dimension with embeddings of a submanifold B with isomorphic normal bundles, we construct a differential graded category from the singular cochains of these spaces, and prove that it is equivalent to the A-infinity category obtained by considering exact Lagrangian embeddings intersecting cleanly along B.

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